# Thread: Maths B question

1. ## Maths B question

The operators of the ferris wheel would like to inject some more excitement into their rides and would like to increase the number of revolutions per minute . Their experience tells them that nausea can occur when riders are subjected to vertical speed in excess of 1m/s. Assist them by using mathematics to estimate the number of revolutions per minute the ferris wheel can go before running the risk of riders being sick all over the place ?

The wheels diameter is 20 metres and it takes 2 minutes to complete one counter-clockwise revolution. Rides last for three revolutions.
I found the h(t)= 10sin(pi/60 t -pi/2)+10
Apparently I can differentiate that to = 1/6 pi sin(pi/60 t)
then make the differentaited equation = 1
then i dont know the right answer for t because I keep getting different answers .
even so what does this t value mean in terms of the whole question ?

HELP PLEASE

2. ## Re: Maths B question

You can do this problem with just algebra. The vertical speed is greatest when the rider is to the side, and so they want the vertical speed to be 1 m/s there. The radius of the wheel is 10m - yeah, they tried to trick us by giving the diameter. The angular speed is then:

$\displaystyle 1\ \frac{\text{m}}{\text{sec}}\ \frac{1\ \text{rev}}{2 \pi 10\ \text{m}}\ \frac{60\ \text{sec}}{1\ \text{min}} = \frac{3}{\pi}$,

or approximately $\displaystyle 0.955\ \frac{\text{rev}}{\text{min}}$.

- Hollywood